We have developed a simple model of the formation of 2-LTR HIV DNA episomes following the addition of integrase inhibitor such as raltegravir to an apparently suppressive antiviral regimen. When 2-LTR concentration data from recent raltegravir intensification experiments is fit to our model, the results strongly suggest that the -LTR episomes are being formed in a compartment where the antiviral drugs are unable to contain HIV replication. The primary research objective of this project is to develop specific testable hypotheses to guide a future clinical validation experiment to confirm these findings. Understanding the mechanisms by which HIV replication may continue in patients with no virus detectable in their blood is critically important to efforts to treat and/or cure HIV infection. If cryptic viremia persists, the HIV-positive patient will eventually develop drug-resistant virus and be forced to switch treatment regimens. The mathematical models developed in the proposed research may provide a minimally invasive experimental method to detect and quantify cryptic viremia. This is a critical first step in being able to study and eliminate this phenomenon in HIV medicine. We will use Bayesian statistics to validate our model against a new dataset, develop model extensions that allow us to plan for other measurements, and develop sampling schedules that optimize the information while minimizing the cost and invasiveness of the experiment.